Question

If $x^2-ax+b=0$ and $x^2-bx+a=0$, then find $a+b$.

Answer 1

We have,

$x^2+ax+b=0......\left(1\right)$

$x^2+bx+a=0......\left(2\right)$

Subtract $\left(1\right)$ from $\left(2\right)$ and we get,

$x(a-b)+(b-a)=0$

$x(a-b)=-(b-a)$

$x(a-b)=(a-b)$

$x=1$

Put the value of $x$ in equation (1) and we get,

$1+a+b=0$

$a+b=-1$

Hence, this is the answer.